On a phenotype-structured phase-field model of nutrient-limited tumour growth

TL;DR

This paper introduces a novel phenotype-structured phase-field model for nutrient-limited tumour growth, capturing cellular heterogeneity and phenotypic evolution, with mathematical analysis and numerical simulations demonstrating key tumor dynamics.

Contribution

It extends existing phase-field models by incorporating phenotypic heterogeneity and evolution, providing a more realistic framework for tumor growth analysis.

Findings

Model is mathematically well-posed under broad conditions

Numerical simulations reveal complex cell dynamics and heterogeneity

Highlights importance of phenotypic evolution in tumor progression

Abstract

Phase-field models of tumour growth have proved useful as theoretical tools to investigate cancer invasion. A key implicit assumption underlying mathematical models of this type which have so far been proposed, though, is that cells in the tumour are identical. This assumption ignores both the fact that cells in the same tumour may express different characteristics to different extents, exhibiting heterogeneous phenotypes, and the fact that cells may undergo phenotypic changes, with their characteristics evolving over time. To address such a limitation, in this paper we incorporate inter-cellular phenotypic heterogeneity and the evolution of cell phenotypes into the phase-field modelling framework. This is achieved by formulating a phenotype-structured phase-field model of nutrient-limited tumour growth. For this model, we first establish a well-posedness result under general assumptions on the model functions, which encompass a wide spectrum of biologically relevant scenarios. We then present a sample of numerical solutions to showcase key features of spatiotemporal and evolutionary cell dynamics predicted by the model. We conclude with a brief overview of modelling and analytical research perspectives.